Factor. 2n^2 + 9n + 9 ____

Question

Bytelearn · Accepted Answer

Identify a, b, c: Identify a, b, and c in the quadratic expression 2n^2 + 9n + 9. Compare 2n^2 + 9n + 9 with the standard quadratic form ax^2 + bx + c. a = 2 b = 9 c = 9Find Factors and Sum: Find two numbers that multiply to a*c (which is 2*9=18) and add up to b (which is 9). We need to find two numbers that satisfy these conditions. After checking possible pairs of factors of 18, we find that there are no such integers that add up to 9.Attempt Factoring: Since we cannot find integers that satisfy the conditions from Step 2, we need to attempt factoring by grouping or use the quadratic formula to check if the quadratic is factorable over the integers. However, since the problem specifically asks for factoring, we will first check if the quadratic can be factored by grouping or if it is a perfect square trinomial.Check Perfect Square Trinomial: Check if the quadratic is a perfect square trinomial. A perfect square trinomial is of the form (ax + b)^2 = a^2x^2 + 2abx + b^2. Comparing 2n^2 + 9n + 9 with a^2x^2 + 2abx + b^2, we can see if 2n^2 is a perfect square, 9n is twice the product of the square root of 2n^2 and some number b, and 9 is the square of b. The square root of 2n^2 is √2n, but 9 is not a perfect square of 2 times any number multiplied by √2n. Therefore, the expression is not a perfect square trinomial.Conclusion: Since the expression is not a perfect square trinomial and we cannot find integers that satisfy the conditions for factoring by grouping, we conclude that the quadratic expression 2n^2 + 9n + 9 cannot be factored over the integers.

Factor. $\newline$ $2n^2 + 9n + 9$

Full solution

More problems from Factor quadratics with other leading coefficients

Related topics

Factor.\newline2n2+9n+92n^2 + 9n + 92n2+9n+9

Factor. $\newline$ $2n^2 + 9n + 9$